# Efficient Estimation of Pauli Channels

@article{Flammia2020EfficientEO, title={Efficient Estimation of Pauli Channels}, author={Steven T. Flammia and Joel J. Wallman}, journal={ACM Transactions on Quantum Computing}, year={2020}, volume={1}, pages={1 - 32} }

Pauli channels are ubiquitous in quantum information, both as a dominant noise source in many computing architectures and as a practical model for analyzing error correction and fault tolerance. Here, we prove several results on efficiently learning Pauli channels and more generally the Pauli projection of a quantum channel. We first derive a procedure for learning a Pauli channel on n qubits with high probability to a relative precision ϵ using O(ϵ-2n2n) measurements, which is efficient in the…

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## References

SHOWING 1-10 OF 197 REFERENCES

Efficient learning of quantum noise

- Physics, Computer Science
- 2020

The results pave the way for noise metrology in next-generation quantum devices, calibration in the presence of crosstalk, bespoke quantum error-correcting codes 10 and customized fault-tolerance protocols 11 that can greatly reduce the overhead in a quantum computation.

Characterizing Noise in Quantum Systems

- Physics, Computer Science
- 2012

A randomized benchmarking protocol is presented that provides a scalable method for determining important properties of the noise affecting the set of gates used on a quantum information processor and various properties ofThe quantum gate fidelity are proved, which is a useful state-dependent measure of the distance between two quantum operations.

Recovering quantum gates from few average gate fidelities

- MathematicsPhysical review letters
- 2018

This Letter provides a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured with respect to random Clifford unitaries for characterizing multiqubit unitary gates.

Performance of quantum error correction with coherent errors

- Computer SciencePhysical Review A
- 2019

This work analytically calculates the effective logical channel that results when the error correction steps are performed noiselessly in quantum error correcting codes and proves a bound on the performance of any stabilizer code when the noise at the physical level is unitary.

Randomized Benchmarking of Quantum Gates

- Computer Science
- 2007

A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate…

Noise tailoring for scalable quantum computation via randomized compiling

- Computer Science
- 2016

This work proposes a method for introducing independent random single-qubit gates into the logical circuit in such a way that the effective logical circuit remains unchanged and proves that this randomization tailors the noise into stochastic Pauli errors, which can dramatically reduce error rates while introducing little or no experimental overhead.

Analysing correlated noise on the surface code using adaptive decoding algorithms

- Computer ScienceQuantum
- 2019

New methods to analyse blue a particular class of spatially correlated errors by making use of parametrised families of decoding algorithms and it is shown that information can be learnt about the parameters of the noise model, and additionally that the logical error rates can be improved.

Efficient Simulation of Random Quantum States and Operators

- Mathematics
- 2005

We investigate the generation of quantum states and unitary operations that are ``random'' in certain respects. We show how to use such states to estimate the average fidelity, an important measure…

Statistical mechanical models for quantum codes with correlated noise

- Computer Science
- 2018

This mapping connects the error correction threshold of the quantum code to a phase transition in the statistical mechanical model, and allows any existing method for finding phase transitions, such as Monte Carlo simulations, to be applied to approximate the threshold of any such code, without having to perform optimal decoding.

Experimental demonstration of Pauli-frame randomization on a superconducting qubit.

- Physics
- 2018

This work uses high-accuracy gate-set tomography to demonstrate that without randomization the natural errors experienced by this experiment have coherent character, and that with randomization these errors are rendered incoherent, and demonstrates how noise models can be shaped into more benign forms for improved performance.